A new cubic convergent method for solving a system of nonlinear equations

ABSTRACT

We present a new cubic convergent method for solving a system of nonlinear equations. The new method can be viewed as a modified Chebyshev's method in which the difference of Jacobian matrixes replaces three order tensor. Therefore, the new method reduces the storage and computational cost. The new method possesses the local cubic convergence as well as Chebyshev's method. A rule is deduced to ensure the descent property of the search direction, and a nonmonotone line search technique is used to guarantee the global convergence. Numerical results indicate that the new method is competitive and efficient for some classical test problems.

KEYWORDS:

• Cubic convergence
• global convergence
• Chebyshev's method
• nonlinear equations
• nonmonotone line search

2010 AMS Subject Classifications:

• 65H10
• 90C53

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grants 11471159,11571169,61661136001; and the Natural Science Foundation of Jiangsu Province under Grant BK20141409.